There isn't really a discrepancy here, I believe. Just a little confusion about the terminology.
When they refer to 195 knots, they are not talking about the nominal touchdown speed, which could easily be 205 or thereabouts, right in the lower-middle of the safety envelope, but about the lowest possible touchdown speed before the Orbiter loses lift, stalls out, and the rear flap impacts the ground.
Weight obviously does matter in considering the minimum touchdown speed, as stated previously. That is clearly indicated in the Hale piece to be dependent on weight, with 195 being standard and 185 being considered the absolute minimum for an underweight Orbiter.
I've checked the NASA stats on landing as you suggested, and in this case there IS a discrepancy. Hale clearly states that he looked at the descent profile analysis "official numbers" and it read 176 knots on touchdown for STS-31. He also states that the commander called him and chewed him out for making him touch down at such a dangerously slow speed. Hale is not a fantastist, he's a credible source. The incident was maybe not all that serious, but rather indicative of the NASA tendency to paper over the cracks when it comes to safety issues.
Meanwhile the official story about STS-37 is dangerously suspect. They say the Orbiter came down 600 feet short, which is not good at all. But Deger, another credible source, says they were 1600 ft or 480 metres short. 600 ft or 1600 ft? In this case the incident could have been very serious indeed. Hale refuses to specify what went on, but drops some very dark hints.
Maybe you prefer to trust the stats but I prefer to trust the testimonies of the people involved here, providing I can get some evidence for them.
BTW, all of this discussion shows that in any case the safe landing speed range is almost incredibly narrow, logically enough given the Shuttle's poor aerodynamic profile. The original Maxime Faget design for the STS wouldn't have had these razor-thin tolerances.